I'll repeat some of what I mentioned in the comments but I'll elaborate a bit as I have more space here.
In my opinion this sounds more like a left hand issue. I do a lot more muting with my left hand, especially during single notes and bends, and only really use my right hand for keeping the lower strings from ringing when playing on the higher strings. Left hand muting really contributes to a better overall sound, especially through an amplified guitar. You need to practice it a lot because electric guitars love to make noise, even when you don't necessarily want them to, so you have to always be aware of what the strings are doing (even the ones you aren't playing). This is done with both hands, but in the beginning I would focus on your left hand muting technique first and really get that down, because that's where the notes are starting and stopping for the most part.
The simple solution for you would be to release the bend before ending the note-- un-bend to the original note then lift your finger. This is a lot easier to do cleanly, especially when you are first learning bending.
There are times though where you will want to release the note at the height of the bend. For this case the best advice I can give is to just lift your finger off the string vertically (perpendicular to the fretboard), so the string doesn't detune before the note is muted. Don't let the string "un-bend" until it stops ringing. When I do it, I sometimes roll my finger back a bit to get it almost under the string to lift the string off the fret and kill the note.. It's hard to describe over text and it's something I only noticed because you asked about how this is normally done. These kinds of things we almost just pick up automatically after a lot of practice. Keep doing the bends, keep working on a clean release, and your hands will probably figure out a way to do it without you having to over-think it too much. It might help to watch some more bending videos to make sure your technique is sound, but more important than that is to just keep playing, this becomes more natural with a lot of practice.
It's also worth noting that a lot of the beauty of bends comes from them not always being "perfect." You seem to be focused on the brief millisecond of release before the note ends, but most listeners probably won't even notice. My orchestra teacher always used to tell me when I was doing vibrato on upright bass that the mind focuses on the highest pitch it hears in a series of small pitch changes, so as long as you are hitting the right note on the peak of the bends, you should be good. With more practice you will get a cleaner sound.